Let's break down the problem based on the information in the image:

1. Sample Space Calculation, $n(S)$:

   • Each die has 6 faces, so when two dice are tossed, there are $6 \times 6 = 36$ possible outcomes.
   • Therefore, $n(S) = 36$.

2. Event $E$:

   • Event $E$ represents the scenario where the sum of the numbers on the two dice equals 7.
   • We need to identify which pairs of dice rolls yield a sum of 7. The possible pairs that satisfy this are:
     • (1, 6)
     • (2, 5)
     • (3, 4)
     • (4, 3)
     • (5, 2)
     • (6, 1)
   • There are 6 such pairs.
   • Therefore, $n(E) = 6$.

3. Probability of Event $E$:

   • The probability of event $E$ is the ratio of $n(E)$ to $n(S)$: $P(E) = \frac{n(E)}{n(S)} = \frac{6}{36} = \frac{1}{6}$

Final Answers:

• $n(S) = 36$
• $n(E) = 6$
• $P(E) = \frac{1}{6}$

Would you like further details, or do you have any questions?

Related Questions:

1. What is the probability of getting a sum of 8 with two dice?
2. How many outcomes produce a sum of 11 in this experiment?
3. If three dice are rolled, what is the total number of outcomes?
4. What is the probability of rolling doubles (same number on both dice)?
5. How many outcomes yield a sum less than 5?

Tip:

For probability questions involving dice, always list the possible pairs for quick verification of outcomes that satisfy given conditions.